What is the correct roster form of X = {x : x ∈ ℕ, x is a divisor of 24, and x² > 24}?
Advertisement
Answer and explanation
Correct answer: X = {6, 8, 12, 24}
The positive natural-number divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. We now apply x² > 24. For x = 1, 2, 3, and 4, the squares are not greater than 24; in particular, 4² = 16. For 6, 8, 12, and 24, the squares exceed 24. Therefore X = {6, 8, 12, 24}, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
X = {6, 8, 12, 24}
Why is this the correct answer?
The positive natural-number divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. We now apply x² > 24. For x = 1, 2, 3, and 4, the squares are not greater than 24; in particular, 4² = 16. For 6, 8, 12, and 24, the squares exceed 24. Therefore X = {6, 8, 12, 24}, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
Advertisement